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We propose a novel Bayesian-Optimistic Frequentist Upper Confidence Bound(BOF-UCB) algorithm for stochastic contextual linear bandits in non-stationaryenvironments. This unique combination of Bayesian and frequentist principlesenhances adaptability and performance in dynamic settings. The BOF-UCBalgorithm utilizes sequential Bayesian updates to infer the posteriordistribution of the unknown regression parameter, and subsequently employs afrequentist approach to compute the Upper Confidence Bound (UCB) by maximizingthe expected reward over the posterior distribution. We provide theoreticalguarantees of BOF-UCB's performance and demonstrate its effectiveness inbalancing exploration and exploitation on synthetic datasets and classicalcontrol tasks in a reinforcement learning setting. Our results show thatBOF-UCB outperforms existing methods, making it a promising solution forsequential decision-making in non-stationary environments.

BOF-UCB: A Bayesian-Optimistic Frequentist Algorithm for Non-Stationary Contextual Bandits